Question

write an equation of the line shown.
7.
8.
9.
write an equation of the line that passes through the given points.

1. $(-10, 7), (5, -3)$
2. $(-5, -3), (12, 17.4)$
3. $(-8, 84), (5, -46)$

write an equation for the linear function $f$ with the given values.

1. $f(4) = -8, f(-3) = 1$
2. $f(6) = -4, f(9) = -9$
3. $f(-1) = -6, f(4) = -14$

Explanation:

Problem 7

Step1: Find slope m

$m = \frac{1-5}{1-0} = \frac{-4}{1} = -4$

Step2: Identify y-intercept b

The line crosses y-axis at $(0,5)$, so $b=5$.

Step3: Write slope-intercept form

$y = mx + b$

Step1: Calculate slope m

$m = \frac{2-(-4)}{-2-(-4)} = \frac{6}{2} = 3$

Step2: Substitute point to find b

Use $(-2,2)$: $2 = 3(-2) + b \implies 2 = -6 + b \implies b=8$

Step3: Write line equation

$y = mx + b$

Step1: Compute slope m

$m = \frac{4-7}{2-(-4)} = \frac{-3}{6} = -\frac{1}{2}$

Step2: Solve for y-intercept b

Use $(2,4)$: $4 = -\frac{1}{2}(2) + b \implies 4 = -1 + b \implies b=5$

Step3: Write slope-intercept equation

$y = mx + b$

Answer:

$y = -4x + 5$

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Problem 8